OPTIMIZATION METHODS ON RIEMANNIAN MANIFOLDS AND THEIR APPLICATION TO SHAPE SPACE

被引：206

作者：

Ring, Wolfgang ^{[1
]}

Wirth, Benedikt ^{[2
]}

机构：

[1] Graz Univ, Inst Math & Sci Comp, A-8010 Graz, Austria

[2] NYU, Courant Inst Math Sci, New York, NY 10012 USA

来源：

SIAM JOURNAL ON OPTIMIZATION | 2012年 / 22卷 / 02期

基金：

奥地利科学基金会;

关键词：

Riemannian optimization; BFGS quasi-Newton; Fletcher-Reeves conjugate gradient; shape space;

D O I：

10.1137/11082885X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We extend the scope of analysis for linesearch optimization algorithms on (possibly infinite-dimensional) Riemannian manifolds to the convergence analysis of the BFGS quasi-Newton scheme and the Fletcher-Reeves conjugate gradient iteration. Numerical implementations for exemplary problems in shape spaces show the practical applicability of these methods.

引用

页码：596 / 627

页数：32

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